Definition:Erlang Distribution
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Definition
Let $X$ be a continuous random variable on a probability space $\struct {\Omega, \Sigma, \Pr}$.
Let $\Img X = \hointr 0 \infty$.
Let $k$ be a strictly positive integer.
Let $\lambda$ be a strictly positive real number.
$X$ is said to have an Erlang distribution with parameters $k$ and $\lambda$ if and only if it has probability density function:
- $\map {f_X} x = \dfrac {\lambda^k x^{k - 1} e^{- \lambda x} } {\map \Gamma k}$
where $\Gamma$ denotes the gamma function.
This is written:
- $X \sim \map {\operatorname {Erlang} } {k, \lambda}$
Also see
- Results about the Erlang distribution can be found here.
Source of Name
This entry was named for Agner Krarup Erlang.
Sources
- Weisstein, Eric W. "Erlang Distribution." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ErlangDistribution.html